Elementary vectors reveal minimal interactions in microbial communities

01.08.2025

Stefan Müller, Michael Predl, Diana Széliová, and Jürgen Zanghellini: Framework for characterizing all feasible microbial interactions

A preprint version from bioRxiv, the preprint server for biology

https://doi.org/10.1101/2025.07.30.667663

 

Abstract

Understanding microbial communities is essential for progress in ecology, biotechnology, and human health. Recently, constraint-based metabolic models of individual organisms have been combined to study microbial consortia. In this work, we present a geometric framework for characterizing all feasible microbial interactions. We project community models onto the key variables of interaction: exchange fluxes and community compositions. Based on this projection, we compute elementary composition/exchange fluxes (ECXs), extending the concept of minimal metabolic pathways from individual species to entire communities. Every feasible metabolic state of a community can be expressed as a combination of these elementary vectors. Notably, each ECX corresponds to a distinct ecological interaction type, such as specialization, commensalism, or mutualism. Finally, our geometric formulation enables the direct application of existing constraint-based methods, such as flux variability analysis and minimal cut sets, to microbial communities, providing a foundation for rational community design.

Microbial community involving species i and j. The corresponding cells (blue and red ovals) maintain their metabolism as given by the internal data, xi, N i, vi and xj, N j, vj, respectively. @ BioRender

Two-species community: (a) reaction network with all (internal and exchange) fluxes and all in/outflows to/from the medium. (b) (in-)equality constraints for exchange fluxes and compositions arising from the steady-state assumption (for the metabolites in the medium and the internal metabolites of the two species) and flux bounds. @ BioRender

Co-culture of M. smithii and B. thetaiotaomicron. Community growth rate vs. mass fraction of M. smithii. @ BioRender